The Arithmetic Intensity of High-Order Discontinuous Galerkin Methods for Hyperbolic Systems

Authors: Suyash Tandon and Eric Johnsen (University of Michigan)

Abstract: High-fidelity numerical simulations of complex flow problems require high-resolution capabilities, which can be achieved by employing high-order methods. A class of recovery-assisted discontinuous Galerkin (RADG) methods can achieve high-orders of accuracy by strategically combining degrees of freedom from neighboring cells; the order of accuracy can be increased by increasing the polynomial degree p of the solution representation. An increase in p, however, increases the number of degrees of freedom, thereby significantly increasing the memory footprint due to I/O operations and floating-point operations. In this study, the arithmetic intensity, which is the amount of work done per data transferred, of a class of RADG methods for hyperbolic systems of conservation laws is theoretically analyzed for p=1 through 6. Different data cache models are considered, and numerical experiments demonstrate that RADG methods have high arithmetic intensity, thus more effectively utilizing on-node floating-point capabilities on modern high-performance computing (HPC) platforms.

Best Poster Finalist (BP): no

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